Higher Order Crossings Analysis of Signals Over Graphs

Panagiotis C. Petrantonakis

Abstract: We propose the extension of the Higher Order Crossings (HOC) analysis concept for signals over graphs. The HOC over graphs sequence, ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$HOC_g$</tex-math></inline-formula> ), is defined and its efficacy on graph signal discrimination is investigated. Compared with state of the art graph signal discrimination algorithms, the proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$HOC_g$</tex-math></inline-formula> combined with a Support Vector Machine classifier achieves fast and similar or better performance over five different benchmark data sets.